I have the -devel package for libx264 installed. Since I haven't been editing video lately, perhaps I updated the package and did not notice. So the resolution is to link libx264.so.54 to the latest libx264. In my case, that happens to be libx264.so.55.

Since I am running 64-bit Fedora, my libraries are in /usr/lib64. Here is the command:ln -s /usr/lib64/libx264.so.55 /usr/lib64/libx264.so.54

Why Mule?

"Mules are not really stubborn. They can seem lazy because they will not put themselves in danger. A horse can be worked until it drops, but not so with a mule. The "stubborn" streak is just the mule's way of telling humans that things are not right. Mules are very intelligent and it is not a good idea to abuse a mule. They will do their best for their owner, with the utmost patience."About Mules